Problem: Solve for $x$ : $6\sqrt{x} - 5 = 8\sqrt{x} + 2$
Solution: Subtract $6\sqrt{x}$ from both sides: $(6\sqrt{x} - 5) - 6\sqrt{x} = (8\sqrt{x} + 2) - 6\sqrt{x}$ $-5 = 2\sqrt{x} + 2$ Subtract $2$ from both sides: $-5 - 2 = (2\sqrt{x} + 2) - 2$ $-7 = 2\sqrt{x}$ Divide both sides by $2$ $\frac{-7}{2} = \frac{2\sqrt{x}}{2}$ Simplify. $-\dfrac{7}{2} = \sqrt{x}$ The principal root of a number cannot be negative. So, there is no solution.